Finite Group Databasebeta

← #29573886

Subgroups — #29573886

Order 15616.

454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454859C211yesmaximal, characteristic
2#21446613C211yesmaximal, characteristic
3C4×#14519693C211yesmaximal, characteristic
4#21444572C211yesmaximal, characteristic, complemented
5#21444571C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1278C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839841—21no—
10#16839841—21no—
11#16839839—21no—
12#16839839—21no—
13#16839815C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519693C411yescharacteristic
16C2×#14519693C411yescharacteristic
17#16839724—22no—
18C2×#14519689—22no—
19C4×#11758194C2211yescharacteristic
20#16839530C411yescharacteristic
21#16839530C411yescharacteristic
22#16839515—21no—
23#16839514—21no—
24#16839513—21no—
25#16839512—21no—
26C61×#431C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61D412yes—
31C2×#11758194C2×C411yescharacteristic
32C2×#11758194C2×C411yescharacteristic
33C2×#11758189—22no—
34C2×#11758189—22no—
35C22×#92418—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198Q812yes—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45C4⋊#92418D411yescharacteristic
46#14519693—22no—
47#14519693—22no—
48C22⋊#92418—21no—
49#14519689—22no—
50#14519689—22no—
51#14519689—44no—
52#14519688—21no—
53C4×#92418—21no—
54C4×#92418—21no—
55C2×M16×C61C2×C411yescharacteristic
56C2×M16×C61C2×C411yescharacteristic
57C22×C8×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61D411yescharacteristic
60C4⋊C8×C61D411yescharacteristic
61C22⋊C8×C61—21no—
62#97×C61—21no—
63C4×C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67C23×D61C4⋊C412yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×Q811yescharacteristic
71C22×Dic61C4⋊C412yes—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82M16×C61—21no—
83M16×C61—21no—
84M16×C61—21no—
85M16×C61M1612yescomplemented
86C2×C8×C61—21no—
87C2×C8×C61—22no—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97#11758198—22no—
98#11758198—22no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101#11758194—21no—
102#11758194—21no—
103#11758194—21no—
104#11758194M1612yescomplemented
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—42no—
110C2×#92418—41no—
111#11758189—82no—
112#11758189—82no—
113C23×C61C2×C4⋊C411yescharacteristic
114C22×D61—22no—
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—42no—
118C22×D61—42no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61C4×D411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61C22⋊Q811yescharacteristic
126C2×C4×C61C22⋊Q811yescharacteristic
127C2×C4×C61#12311yescharacteristic
128C2×C4×C61C2×M1611yescharacteristic
129C2×C4×C61C2×M1611yescharacteristic
130C2×C4×C61#13111yescharacteristic
131C2×C4×C61#13111yescharacteristic
132C2×Dic61—22no—
133C2×Dic61—42no—
134D244—41no—
135D244—41no—
136D244—41no—
137D244—41no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—82no—
141C8×C61—22no—
142C8×C61—42no—
143C8×C61—41no—
144C8×C61—41no—
145C8×C61—41no—
146#92418—22no—
147#92418—41no—
148#92418—41no—
149#92418—41no—
150#92418—81no—
151#8837—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61#38511yescharacteristic
155C22×C61#42311yescharacteristic
156C22×C61#42411yescharacteristic
157C2×D61—44no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—82no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61#43511yescharacteristic
166C4×C61#43511yescharacteristic
167C4×C61#43611yescharacteristic
168C4×C61#43611yescharacteristic
169C4×C61#45311yescharacteristic
170C4×C61#45511yescharacteristic
171Dic61—42no—
172#2975—611no—
173#1954—611no—
174C4×#100—611no—
175#1565—611no—
176#1565—611no—
177#1278—611no—
178#1278D6111yescharacteristic, complemented
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#185111yescharacteristic
182C2×C61#185611yescharacteristic
183C2×C61#185811yescharacteristic
184D61—82no—
185C2×C4×D4—611no—
186#436—1221no—
187#436—1221no—
188#436—1221no—
189#436—1221no—
190#431—611no—
191#431C2×D6111yescharacteristic
192C2×C4⋊C8—611no—
193C2×#100—611no—
194C2×#100—611no—
195#407—1222no—
196C2×C22⋊C8—1222no—
197C4×M16—611no—
198C4×M16C2×D6111yescharacteristic
199C2×C4×C8C2×D6111yescharacteristic
200#343—611no—
201#343—611no—
202#335—1221no—
203#335—1221no—
204#334—1221no—
205#334—1221no—
206C61#883711yescharacteristic, complemented, Sylow
207C22×D4—611no—
208C23×C4—612no—
209C2×M16—611no—
210C2×M16—611no—
211C2×M16—1222no—
212C2×M16—1222no—
213C2×M16C4×D6111yescharacteristic
214C2×M16C4×D6111yescharacteristic
215C22×C8—21no—
216C22×C8—1221no—
217C4×D4—1221no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221C2×C4⋊C4—611no—
222C2×C22⋊C4—612no—
223C2×C42C22×D6111yescharacteristic
224C4⋊C8—611no—
225C4⋊C8—611no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8D24411yescharacteristic
229C4⋊C8D24411yescharacteristic
230#100—1222no—
231#100—1222no—
232C22⋊C8—21no—
233C22⋊C8—1222no—
234C22⋊C8—1222no—
235C22⋊C8—1221no—
236C22⋊C8—2444no—
237#97—21no—
238#97—1221no—
239C4×C8—21no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8—1221no—
244C4×C8—1221no—
245C24—612no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4—1221no—
252C22×C4—612no—
253C22×C4—1222no—
254C22×C4—1222no—
255C22×C4—2442no—
256C22×C4—2442no—
257C22×C4C2×C4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C22×C4Q8×D6111yescharacteristic
260M16—21no—
261M16—21no—
262M16—21no—
263M16—612no—
264M16—1221no—
265M16—1221no—
266M16—1221no—
267M16—4882no—
268M16—4882no—
269M16#1175818912yescomplemented
270C2×C8—21no—
271C2×C8—22no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—2442no—
282C2×C8—2441no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C22⋊C4—1222no—
286C22⋊C4—1222no—
287C42C2×D24411yescharacteristic
288C42#1175822211yescharacteristic
289C42D4×D6111yescharacteristic
290C42#1175822411yescharacteristic
291C23—1222no—
292C23—1222no—
293C23—1222no—
294C23—2442no—
295C23—2442no—
296C23C4⋊C4×D6111yescharacteristic
297D4—2441no—
298D4—2441no—
299D4—2441no—
300D4—2441no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—1222no—
305C2×C4—4882no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4#1451973711yescharacteristic
310C2×C4C4×D24411yescharacteristic
311C2×C4#1451974711yescharacteristic
312C2×C4#1451975511yescharacteristic
313C2×C4#1451975711yescharacteristic
314C2×C4#1451975911yescharacteristic
315C2×C4M16×D6111yescharacteristic
316C2×C4C2×#1175818911yescharacteristic
317C2×C4#1451978311yescharacteristic
318C2×C4#1451978511yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—41no—
323C8—41no—
324C8—1222no—
325C8—4881no—
326C8—2441no—
327C8—2441no—
328C8—2441no—
329C22—21no—
330C22—21no—
331C22—4882no—
332C22—2444no—
333C22—2442no—
334C22—2442no—
335C22—2442no—
336C22#1683963611yescharacteristic
337C22#1683978411yescharacteristic
338C22#1683978711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—2442no—
343C4#1683983011yescharacteristic
344C4#1683983511yescharacteristic
345C4#1683983711yescharacteristic
346C4#1683984111yescharacteristic
347C4#1683993111yescharacteristic
348C4#1683994111yescharacteristic
349C2—21no—
350C2—21no—
351C2—4882no—
352C2#2144600311yescharacteristic
353C2#2144603011yescharacteristic
354C2#2144604011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1278C2
socleC22×C61#385
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1278D61
hypocenterC61#8837
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21444572C2semidirect
5. #21444571C2semidirect
6. #21443656C2semidirect
7. C61×#1278C2semidirect
85. M16×C61M16semidirect
104. #11758194M16semidirect
178. #1278D61semidirect
206. C61#8837semidirect
269. M16#11758189semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214548592
#214466132
C4×#145196932
#214445722
#214445712
#214436562
C61×#12782
#883761